The determinant Delta=|{:(,a^(2)(1+x),ab...

The determinant `Delta=|{:(,a^(2)(1+x),ab,ac),(,ab,b^(2)(1+x),(bc)),(,ac,bc,c^(2)(1+x)):}|` is divisible by

A

`x+3`

B

`(1+x)^(2)`

C

`x^(2)`

D

`x^(2)+1`

Text Solution

Verified by Experts

The correct Answer is:

A, C

Topper's Solved these Questions

MATRICES & DETERMINANT
RESONANCE|Exercise EXERCISE-2|20 Videos
MATRICES & DETERMINANT
RESONANCE|Exercise PART-IV|6 Videos
MATRICES & DETERMINANT
RESONANCE|Exercise PART-II|27 Videos
INDEFINITE INTEGRATION
RESONANCE|Exercise SELF PRACTIC PROBLEMS|25 Videos
NUMBER THEORY
RESONANCE|Exercise Exercise -2 (PART - II)|4 Videos

Similar Questions

Explore conceptually related problems

The determinant Delta=|{:(a^(2)+x^(2),ab,ac),(ab,b^(2)+x^(2),bc),(ac,bc,c^(2)+x^(2)):}| is divisible by

The determinant Delta = |(a^(2) + x^(2),ab,ac),(ab,b^(2) + x^(2),bc),(ac,bc,c^(2) + x^(2))| is divisible

Without expanding the determinant, show that the determinant |{:(a^(2)+10,ab,ac),(ab,b^(2)+10,bc),(ac,bc,c^(2)+10):}| is divisible by 100

What is |{:(-a^(2),ab,ac),(ab,-b^(2),bc),(ac,bc,-c^(2)):}| equal to ?

What is the value of |(-a^(2),ab,ac),(ab,-b^(2),bc),(ac,bc,-c^(2))| ?

Prove that |{:(a^(2)+1,ab,ac),(ab,b^(2)+1,bc),(ac,bc,c^(2)+1):}|=1+a^(2)+b^(2)+c^(2) .

the determinant Delta=|[a^2+x, ab, ac] , [ab, b^2+x, bc] , [ac, bc, c^2+x]| is divisible by

The determinat Delta=|(b^2-ab,b-c,bc-ac),(ab-a^2,a-b,b^2-ab),(bc-ac,c-a,ab-a^2)| equals

if a,b,c are real then find the intervial in which f(x)=|{:(x+a^2,ab,ac),(ab,x+b^2,bc),(ac,bc,x+c^2):}| is decreasing.

RESONANCE-MATRICES & DETERMINANT-PART-III

Text Solution
|
Which one of the following is wrong?
Text Solution
|
Which of the following is true for matrox A=[{:(,1,-1),(,2,3):}]
Text Solution
|
Suppose a(1),a(2),a(3) are in A.P. and b(1),b(2),b(3) are in H.P. and ...
Text Solution
|
Let theta=(pi)/(5),X=[{:(,cos theta,-sin theta),(,sin theta,cos theta)...
Text Solution
|
If Delta=|{:(,x,2y-z,-z),(,y,2x-z,-z),(,y,2y-z,2x-2y-z):}|,then
Text Solution
|
Let a.b ,gt 0 and Delta=|{:(,-x,a,b),(,b,-x,a),(,a,b,-x):}|, then
Text Solution
|
The determination Delta=|{:(,b,c,balpha+c),(,c,d,calpha+d),(,balpha+c,...
Text Solution
|
The determinant Delta=|{:(,a^(2)(1+x),ab,ac),(,ab,b^(2)(1+x),(bc)),(,a...
Text Solution
|
If a non-singular matrix and A^(T) denotes the tranpose of A, then
Text Solution
|
Let "Let"(x)=|{:(,2sinx,sin^(2)x,0),(,1,2sin x,sin^(2)x),(,0,1,2sin x)...
Text Solution
|
Let Delta=|{:(,1,x,x^(2)),(,x^(2),1,x),(,x,x^(2),1):}|,then
Text Solution
|
Let f(x)=|{:(,1//x,logx,x^(n)),(,1,-1//n,(-1)^(n)),(,1,a,a^(2)):}| whe...
Text Solution
|
If D is determinant of order three of Delta is a determinant formed by...
Text Solution
|
Let A,B,C,D be real matrices such that A^(T)=BCD,B^(T)=CDA,C^(T)=DAB a...
Text Solution
|
Let A and B be two 2 xx 2 matrix with real entries, If AB=0 and such t...
Text Solution
|
If A^(-1)=[{:(,1,-1,0),(,0,-2,1),(,0,0,-1):}] then
Text Solution
|
IF A and B are squre matrices of order 3, then the true statement is/a...
Text Solution
|
Let M be a 3xx3 non-singular matrix with det(M)=4,"If" M^(-1)"adj(adjM...
Text Solution
|
Let AX=B where A is 3 xx 3 and X and B are 3 xx 1 matrices then which ...
Text Solution
|